Oberwolfach Seminar: Algebraic Properties of Profinite Groups

June 12th - June 18th, 2011
Nikolay Nikolov, London
Dan Segal, Oxford

An introduction to profinite groups from an algebraic (group-theoretic) point of view. The aims are

  1. to explain various methods that have been used recently to illuminate the algebraic properties of finitely generated profinite groups,
  2. to explore the consequences, both for profnite groups and for infinite group theory in general, and
  3. to explore which profinite groups can be the profinite completions of finitely generated (abstract) groups.

Major results to be covered (in the lectures or in the examples classes) will include the solution of Serre's problem on finite-index subgroups in finitely generated profinite groups (due to Nikolov and Segal); related results about verbal width in pro-p groups (due to Jaikin-Zapirain); the theorem of Jarden and Lubotzky on elementary equivalence of profinite groups; The theorem of Nori and Weisfeiler on strong approximation for linear groups, and its application to polynomial subgroup growth groups by Lubotzky and Mann.

Not all will be proved in full: the emphasis will be on understanding the underlying ideas and exploring the implications.

Preparatory reading

In most cases, it will suffice to understand the main definitions and the statements of the main theorems: you are not expected to work through all the proofs.

Deadline for applications
April 15th, 2011

The seminars take place at the Mathematisches Forschungsinstitut Oberwolfach. The number of participants is restricted to 25. The Institute covers accommodation and food. We are pleased that the Carl Friedrich von Siemens Foundation has decided to support the Oberwolfach Seminars from summer 2008 to summer 2013. By this support, travel expenses can be reimbursed up to 200 Euro in average per person. Participants can ask for travel support during their stay in Oberwolfach at the guest office against copy of travel receipts. Applications including

should be sent preferably by e-mail (.ps or .pdf file) to:

    Prof. Dr. Dr. h.c. Gert-Martin Greuel
    Universität Kaiserslautern
    Fachbereich Mathematik
    Erwin Schrödingerstr.
    67663 Kaiserslautern, Germany

Mathematisches Forschungsinstitut Oberwolfach   updated: January 26th, 2011